The equation of a parabola is y = x^2 - 2x + 7. Write the equation in vertex form. Write any numbers as integers or simplified proper or improper fractions. ______

Identify vertex form: Identify the vertex form of a parabola. The vertex form of a parabola is given by the equation y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.Complete the square: Complete the square to rewrite the given equation in vertex form. We have the equation y = x^2 - 2x + 7. To complete the square, we need to find the value that makes x^2 - 2x a perfect square trinomial. We do this by taking half of the coefficient of x, squaring it, and adding it to and subtracting it from the equation. Half of the coefficient of x is -2/2 = -1. Squaring this gives us (-1)^2 = 1. We add and subtract 1 to the equation.Add and subtract: Add and subtract the squared term to the equation. y = x^2 - 2x + 1 + 7 - 1 Now we have the perfect square trinomial x^2 - 2x + 1 and the constants 7 - 1 outside.Factor and simplify: Factor the perfect square trinomial and simplify the constants. y = (x - 1)^2 + 6 We have factored x^2 - 2x + 1 into (x - 1)^2 and combined 7 - 1 into 6.

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The equation of a parabola is $y = x^2 - 2x + 7$ . Write the equation in vertex form. $\newline$ Write any numbers as integers or simplified proper or improper fractions. $\newline$ ______

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Algebra 1

Write a quadratic function in vertex form

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Q. The equation of a parabola is

y = x^2 - 2x + 7

. Write the equation in vertex form.

\newline

Write any numbers as integers or simplified proper or improper fractions.

\newline

______

Identify vertex form: Identify the vertex form of a parabola. $\newline$ The vertex form of a parabola is given by the equation $y = a(x - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Complete the square: Complete the square to rewrite the given equation in vertex form. $\newline$ We have the equation $y = x^2 - 2x + 7$ . To complete the square, we need to find the value that makes $x^2 - 2x$ a perfect square trinomial. We do this by taking half of the coefficient of $x$ , squaring it, and adding it to and subtracting it from the equation. $\newline$ Half of the coefficient of $x$ is $-2/2 = -1$ . Squaring this gives us $(-1)^2 = 1$ . We add and subtract $1$ to the equation.
Add and subtract: Add and subtract the squared term to the equation. $\newline$ $y = x^2 - 2x + 1 + 7 - 1$ $\newline$ Now we have the perfect square trinomial $x^2 - 2x + 1$ and the constants $7 - 1$ outside.
Factor and simplify: Factor the perfect square trinomial and simplify the constants. $\newline$ $y = (x - 1)^2 + 6$ $\newline$ We have factored $x^2 - 2x + 1$ into $(x - 1)^2$ and combined $7 - 1$ into $6$ .